With regard to an arrangement in which a stabilizer bush is fitted around the outer periphery of a torsion portion of a stabilizer that connects left and right suspension systems, and the stabilizer bush is supported on a vehicle body in a state in which it is clamped by a bracket and compressed radially inwardly, one in which an axially extending cutout part is formed in an outer peripheral face of the stabilizer bush to thus decrease the contact surface pressure on an outer peripheral face of the torsion portion and enable the torsion portion to easily rotate relative to the stabilizer bush, thereby preventing the occurrence of abnormal noise, is known from Patent Publication 1 below.    Patent Publication 1: Japanese Patent Application Laid-open No. 11-291736